Question: Solve for $x$ and $y$ using elimination. ${3x+y = 34}$ ${5x-y = 30}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $8x = 64$ $\dfrac{8x}{{8}} = \dfrac{64}{{8}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {3x+y = 34}\thinspace$ to find $y$ ${3}{(8)}{ + y = 34}$ $24+y = 34$ $24{-24} + y = 34{-24}$ ${y = 10}$ You can also plug ${x = 8}$ into $\thinspace {5x-y = 30}\thinspace$ and get the same answer for $y$ : ${5}{(8)}{ - y = 30}$ ${y = 10}$